The tremor, which could be felt in the capital Taipei, hit at 7:35 am (2335 GMT) at a depth of 15 kilometres (about nine miles) near Hualien, epicentre of a major quake in April, according to the USGS.
Taiwan's Central Weather Administration, which initially reported a 6.3-magnitude quake, issued a mobile phone alert warning people to "keep calm and seek cover nearby".
In Hualien, two people trapped in elevators during the quake were rescued, according to the local fire bureau.
But the National Fire Agency said there was no major damage and that the island's high-speed trains, rail and metro systems were all operating normally.
Still, the government urged vigilance in the wake of a 5.4-magnitude quake that triggered an alert on Thursday.
"In response to the continuous earthquakes, the Ministry of the Interior called on the public to remain vigilant, pay attention to the occurrence of aftershocks, and be prepared for earthquakes," it said in a statement.
Taiwan experiences frequent earthquakes due to its location between two tectonic plates.
The last major one occurred in early April when the island was hit by a deadly 7.4-magnitude tremor that officials said was the strongest in 25 years.
At least 17 people were killed in that quake, which triggered landslides and severely damaged buildings around Hualien.
April's earthquake was the most serious in Taiwan since it was struck by a 7.6-magnitude tremor in 1999.
Some 2,400 people died in that quake, making it the deadliest natural disaster in the island's history.
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